To solve this, let's analyze the transformation of the function $y = f(x)$ into $y = f(x - 4) + 3$.

1. Transformation of $x$ to $x - 4$:

   • When we replace $x$ with $x - 4$, this results in a horizontal shift of the graph.
   • The graph is shifted 4 units to the right. This is because when the input $x$ is decreased by 4 (i.e., $x - 4$), the function is "delayed" by 4 units, meaning each point on the graph moves to the right by 4 units.

2. Transformation of the function to $f(x) - 4 + 3$ (or $+ 3$):

   • Adding a constant (like +3) outside the function shifts the graph vertically.
   • The graph is shifted 3 units up, as adding a constant to the function increases its output for every input.

Thus, the transformation involves a shift of 4 units to the right and 3 units up.

The correct answer is:

c. Shifting the given graph 4 units to the right, then 3 units up.

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Would you like more details on transformations of functions, or do you have other questions? Here are some related questions to explore:

1. How does the graph of $y = f(x + 4)$ compare to the graph of $y = f(x)$?
2. What happens when you shift a graph horizontally and vertically simultaneously?
3. Can transformations like this be applied to trigonometric functions like $y = \sin(x)$?
4. How do reflections across the x-axis or y-axis affect the graph of a function?
5. How would you interpret the transformation $y = f(x + 2) - 5$?

Tip: When analyzing transformations, remember that a change to $x$ affects horizontal movement, while changes to the function (like adding or subtracting constants) affect vertical shifts.